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Mirrors > Home > MPE Home > Th. List > exbi | Structured version Visualization version GIF version |
Description: Theorem 19.18 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.) |
Ref | Expression |
---|---|
exbi | ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓)) | |
2 | 1 | alexbii 1760 | 1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 196 ∀wal 1481 ∃wex 1704 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 |
This theorem depends on definitions: df-bi 197 df-ex 1705 |
This theorem is referenced by: exbii 1774 nfbiit 1777 19.19 2097 bj-2exbi 32599 bj-3exbi 32600 2exbi 38579 rexbidar 38650 onfrALTlem5VD 39121 onfrALTlem1VD 39126 csbxpgVD 39130 csbrngVD 39132 csbunigVD 39134 e2ebindVD 39148 e2ebindALT 39165 |
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